Unfortunately they only provide the latest 120 likes in newest-to-oldest order with no pagination. You can test this by requesting a photo then liking it and you'll see that your account is on top of the list.

The only work around is to set up a job to periodically cache likes beginning shortly after the photo is first posted. Since you're always getting the newest 120 you can get them all that way. You can create a subscription to a user using the realtime api and get a ping when your user posts a new photo, then start caching likes. A decaying rate would be advised - maybe cache a couple times the first hour after it's posted, then less and less frequently the longer it's been.